查看更多>>摘要：In this paper, the eigenvalue problem for the class of quasi-generalized Vandermonde (q-gV) matrices is considered. In order to parameterize q-gV matrices, the explicit expressions of minors of such matrices are presented. We develop an algorithm to accurately compute the parameterization for q-gV matrices. Relying on the accurate parameterization, all the eigenvalues of q-gV matrices are computed to high relative accuracy. Error analysis and numerical experiments are provided to confirm the high relative accuracy. (C)& nbsp;2021 Elsevier B.V. All rights reserved.& nbsp;
查看更多>>摘要：Numerical approximation of stochastic Stokes-Darcy equations usually requires repeated sampling of the random hydraulic conductivity tensor and then simulating flow ensembles. In this setting, we propose an efficient, second order, ensemble algorithm for fast computation of the whole set of realizations of the stochastic Stokes-Darcy model corresponding to different random hydraulic conductivity tensor samples. The ensemble algorithm only requires the solution of two linear systems that have the same constant coefficient matrices for all realizations. We give a complete long time stability and convergence analysis for the method. Numerical experiments are presented to support theoretical results and demonstrate the application of the method. (C)& nbsp;2021 Elsevier B.V. All rights reserved.& nbsp;
查看更多>>摘要：This study proposes a new methodology to analyze the impacts of host and pathogen dispersal on coinfection dynamics using the example of Escherichia coli O157:H7 in a dairy farm. A multi-strain Susceptible-Infected-Susceptible model is extended to a Reaction-Diffusion (RD) coinfection model of E. coli O157:H7 transmission, which includes intermittent shedding and pathogen growth in the environment. Analysis of the new RD coinfection model consists of existence and stability of constant equilibria, calculation of the basic reproduction number, and existence of traveling and stationary wave solutions. A stationary wave solution of the RD model defines a nonconstant endemic equilibrium. Whereas a traveling wavefront represents an epidemic wave of infection passing through the farm with a specific speed, direction, and amplitude. The numerical simulations of the RD model demonstrate stable traveling and stationary wavefronts of the RD coinfection model. The stationary wavefront connects two constant coexistence equilibria and the traveling wavefront represents the gradual establishment of an endemic coexistence equilibrium in the dairy farm. The significance of this study lies in utilizing the nonlinear wave theory to analyze dynamics of coinfection in a dairy farm both with respect to location and time. Hence, in addition to Turing theory, the nonlinear wave theory can be used to determine the likelihood of acquiring the infection based on the location of cattle at each specific time. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：This paper introduces an efficient approach to solve quadratic and nonlinear programming problems subject to linear equality constraints via the theory of functional connections. This is done without using the traditional Lagrange multiplier technique. In particular, two distinct expressions (fully satisfying the equality constraints) are provided, to first solve the constrained quadratic programming problem as an unconstrained one for closed-form solution. Such expressions are derived by utilizing an optimization variable vector, which is called the free vector g by the theory of functional connections. In the spirit of this theory, for the equality constrained nonlinear programming problem, its solution is obtained by the Newton's method combining with elimination scheme in optimization. Convergence analysis is supported by a numerical example for the proposed approach.(C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：Compressed sensing magnetic resonance imaging (CS-MRI) makes it possible to shorten data acquisition time substantially. The traditional iteration-based CS-MRI method is flexible in modeling but is usually time-consuming. Recently, the deep neural network method becomes popular in CS-MRI due to its high efficiency. However, the drawback of the deep learning method is inflexibility. It depends overly on the training images and scanning method of the k-space data. In this paper, we propose an iterative method for MRI reconstruction, called IDPCNN, combining the merits of both the traditional method and the deep learning methods, realizing quick, flexible, and accurate reconstruction. The proposed method incorporates two stages: denoising and projection. The denoising step employs a state-of-the-art denoiser to smooth the image. The projection step explores the prior information from the frequency domain and adds details to the spatial domain iteratively. The reconstruction quality is superior to the best MRI reconstruction methods under different sampling masks and rates. The stability, speed, and good reconstruction quality mean that our IDPCNN has the potential for widespread clinical applications. (C)& nbsp;2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：The well-known approximation formula by Barone-Adesi and Whaley (BAW) for pricing American options works well for contingent claims in the current business environment with low rates, but it lacks precision for pricing options when interest rates are high or in case of turmoil. In this paper, we introduce a new closed formula that is the solution of a non-autonomous PDE instead of the classical ODE. Our improved solution performs well in case of high turbulence allowing traders and risk managers to run stress tests with an appropriate model. This is complemented by an analytical approximation of the critical stock price S* as well as of the implied volatility. When a shock comes, it might be helpful to have the right model to deal with it. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：The main purpose of this article is to solve the pantograph Volterra delay integrodifferential equation of fractional order. A numerical operational matrix approach based on Euler wavelets is proposed. For the proposed scheme, the fractional integral operational matrix is constructed. Then the pantograph Volterra delay integro-differential equations are reduced to algebraic equations by using the fractional integral operational matrix. Several theorems are presented to establish the convergence and error analysis of the proposed method. To show the accuracy of the proposed technique, the numerical convergence rate has been shown. Additionally, some numerical problems are solved to justify the applicability and validity of the presented technique. Also, the numerical results have been documented graphically to describe the effectiveness of the approach. Furthermore, comparing numerical results with those obtained by known methods shows that the approach scheme is more efficient and accurate. (c) 2021 Elsevier B.V. All rights reserved.
Kuczynski, M. D.Borchardt, M.Kleiber, R.Koenies, A....
8页
查看更多>>摘要：We present a Fourier-decomposition-based approach aided by a Neural Network for the classification of the eigenfunctions of an operator appearing in ideal magnetohydrodynamics. The Neural Network is trained on individual Fourier modes, which enhances the robustness of the classification. In our tests, the algorithm correctly classified 93.5% of the data and returned the remaining 6.5% for manual classification. The probability of misidentifying the eigenfunctions is estimated as 0.03%. The discussion is kept quite general allowing for potential applications in other fields. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper we design a family of fully implicit strong Ito-Taylor numerical methods for stochastic differential equations (SDE). These methods are based on the truncation of our general stochastic Ito-Taylor expansions, in which the truncation can be chosen to make our methods converge with high order. And by selecting the parameters in the methods, we can get methods with different stability. The mean-square (MS) stability of the second-order case is investigated. Numerical results are reported to show the convergence properties and the stability properties of our methods.(C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：This paper deals with the design and analysis of a high order numerical scheme for the nonlinear time-fractional generalized Fisher's equation (TFGFE). The Caputo fractional derivative (FD) of order alpha, (alpha is an element of (0, 1)) appearing in the model problem is approximated by means of L1 - 2 scheme. The discretization for the space derivative is made by a collocation method based on quintic B-spline (QBS) basis function. Convergence analysis of the method is established. Five examples are provided to demonstrate the efficiency and feasibility of the method. The influence of alpha on the solution profile of the TFGFE is examined. It is shown that our method is of O(Delta t(2) + Delta x(4)) accuracy, where Delta t and Delta x respectively represent the time and space step sizes. The results obtained are compared with those of other three methods. The CPU time (in seconds) is given in order to justify the computational efficiency of proposed numerical scheme. (C) 2021 Elsevier B.V. All rights reserved.
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